On the Sitnikov Problem
Abstract
A mapping which reflects the properties of the Sitnikov problem is derived. We study the mapping instead of the original differential equations and discover that there exists a hyperbolic invariant set. The theoretical prediction of the disorder region agrees remarkably with numerical results. We also discuss the LCEs and KSentropy of the dynamical system.
 Publication:

Celestial Mechanics and Dynamical Astronomy
 Pub Date:
 September 1990
 DOI:
 10.1007/BF00049419
 Bibcode:
 1990CeMDA..49..285L
 Keywords:

 Equations Of Motion;
 Hyperbolic Differential Equations;
 Stellar Motions;
 Three Body Problem;
 Celestial Mechanics;
 Center Of Mass;
 Computational Astrophysics;
 Elliptical Orbits;
 Entropy;
 Transformations (Mathematics);
 Astrophysics;
 Dynamical systems;
 Sitnikov problem;
 KSentropy;
 hyperbolic invariant set